The pantograph has a long history in kinematics; it is one of the oldest multi-link examples of displacement magnification. Early uses were for transcription, then for collapsible structures, and even for children's toys. Many pantograph-style linkages have been developed using multiple pantograph-like units that obey certain geometric restrictions, but have yet to be described in a general fashion.
U.S. Pat. No. 244,215 titled “Camp stool” by inventor Joseph Beverley Fenby issued Jul. 12, 1881, and is incorporated herein by reference. This patent describes rectangular pantograph elements used to construct a camp stool.
U.S. Pat. No. 764,224 titled “Trolley” by inventor John Quincy Brown issued Jul. 5, 1904, and is incorporated herein by reference. The patent describes a pantograph used for electrical power transmission from overhead lines for electric trains.
U.S. Pat. No. 3,672,104 titled “Nesting Three Dimensional Lazy Tong Structure” by inventor George R. Luckey issued Jun. 27, 1972, and is incorporated herein by reference. The patent describes a nesting three-dimensional lazy tong structure of hollow polygonal cross-section having tapered sides provided by lazy tong frames whose hinged links are pivotally joined and cross-over one another in a manner such that the successive link sets or tiers of the structure nest one within the other when the structure is retracted to its contracted configuration to provide the structure with a contracted length approximating the contracted dimension of a single link set or tier. A lazy tong frame and link pair for the structure.
U.S. Pat. No. 4,942,700 titled “Reversibly expandable doubly-curved truss structure” by inventor Charles Hoberman issued Jul. 24, 1990, and is incorporated herein by reference. This patent describes a loop-assembly is disclosed which is comprised of at least three scissors-pairs, at least two of the pairs comprising: two essentially identical rigid angulated strut elements each having a central and two terminal pivot points with centers which do not lie in a straight line, each strut being pivotally joined to the other of its pair by their central pivot points, each pair being pivotally joined by two terminal pivot points to two terminal pivot points of another pair in that, (a) the terminal pivot points of each of the scissors-pairs are pivotally joined to the terminal pivot points of the adjacent pair such that both scissors-pairs lie essentially in the same plane, or (b) the terminal pivot points of a scissors-pair are each pivotally joined to a hub element which is small in diameter relative to the length of a strut element, and these hub elements are in turn joined to the terminal pivot points of another scissors-pair, such that the plane that one scissors-pair lies in forms an angle with the plane that the other scissors-pair lies in, the axes passing through the pivot points of one of the scissors-pair not being parallel to the axes of the other scissors-pair, where a closed loop-assembly is thus formed of scissors-pairs, and this loop-assembly can freely fold and unfold without bending or distortion of any of its elements, and a line that intersects and is perpendicular to the axes of any two terminal pivot points is non-parallel with at least two other similarly formed lines in the assembly, the angles formed between said lines remaining constant as the loop-assembly is folded and unfolded.
U.S. Pat. No. 3,124,387 titled “Seating structures” by inventor Owen Finlay Maclaren issued Mar. 10, 1964, and is incorporated herein by reference. This patent describes the use of pantograph elements with offset pin joints to construct a folding seating structure.
U.S. Pat. No. 4,193,415 titled “Umbrella canopy frame and staff construction” by inventor Terry Hermanson issued Mar. 18, 1980, and is incorporated herein by reference. This patent describes umbrella construction comprising first and second hub members in combination with a canopy frame member and a staff member, the hub members being spaced-apart from each other on opposite sides of the staff member, independent of each other, and provided with a plurality of holes, the staff member including two series of links forming a lazy-tong device adapted to fold together into closed condition and to unfold into opened condition, the two series of links each having an upper link unit pivotally connected to the upper link unit of the other at the upper ends thereof when the staff means is in opened condition, one of the hub members being secured to the upper link unit of one of the series of links adjacent the upper end thereof, the other of the hub members being secured to the upper link unit of the other of the series of links adjacent the upper end thereof and on a side of the staff member opposite from the one of the hub members. The canopy frame member includes a circumferentially extending series of pairs of ribs, each rib of the pairs being pivotally connected to the other at a point intermediate the opposite ends thereof. A plurality of spokes each have a radially inner end extending in a separate one of the holes of the hub members and a radially outer end pivotally secured to a separate pair of the ribs at the intermediate point thereof.
U.S. Pat. No. 23,503 titled “Umbrella” by inventor L. K. Selden issued Apr. 5, 1859, and is incorporated herein by reference. This patent describes a folding umbrella frame.
U.S. Pat. No. 5,761,871 titled “Framework structure” by inventor Katsuhito Atake issued Jun. 9, 1998, and is incorporated herein by reference. This patent describes a framework structure comprises three or more primary constituent units each including two rigid diagonal members constituting the diagonals of a quadrangular lateral face of a solid and coupled together for relative rotation about a first rotation axis passing through the intersection of the diagonals. The primary constituent units are coupled to one another via second and third rotation axes into a ring-like form. A more complicated framework structure can be obtained by using a plurality of these framework structures as secondary constituent units which are coupled to one another with a coupler or a primary constituent unit used in common between adjacent ones of the secondary constituent units. The framework structure can provide one which is capable of being expanded and contracted in three-dimensional directions and which has rigidity in any directions.
U.S. Pat. No. 5,024,031 titled “Radial expansion/retraction truss structures” by inventor Charles Hoberman issued Jun. 18, 1991, and is incorporated herein by reference. This patent describes a loop-assembly is disclosed which is comprised of at least three scissors-pairs, at least two of the pairs comprising: two essentially identical rigid angulated strut elements, each having a central and two terminal pivot points which do not lie in a straight line, each strut being pivotally joined to the other of its pair by their central pivot points, each pair being pivotally joined by two terminal pivot points to two terminal pivot points of another pair such that both scissors pairs lie essentially in the same plane, or each pair being pivotally joined by two terminal pivot points to two terminal pivot points of another pair in that the terminal points of a scissors-pair are each pivotally joined to a hub element, and these hub elements are in turn joined to the terminal pivot points of another scissors-pair, whereby a closed loop-assembly is thus formed of scissors pairs, and this loop-assembly can fold and unfold, and a line that intersects and is perpendicular to the axes of any two terminal pivot points is non-parallel with at least two other similarly formed lines in the assembly, the angles formed between said lines remaining constant as the loop assembly is folded and unfolded.
U.S. Pat. No. 5,657,584 titled “Concentric joint mechanism” by inventor Gregory J. Hamlin issued Aug. 19, 1997, and is incorporated herein by reference. This patent describes a joint mechanism having a movement between relative members about a center of rotation located at a point where a first line extends from one of the members intersects a second line extending from the opposite member is disclosed. Multiple joint mechanisms may be aligned together along with common lines being the axis of rotation of each joint mechanism to provide a concentric spherical joint mechanism. Concentric spherical joint mechanism may be used to assemble truss frame structures.